Chapter 2 — Answers
Selected answers for Chapter 2: The Nature of Deductive Reasoning, transcribed from the book’s appendix. They are meant for checking your work, not for copying — the book prints answers to selected exercises only.
Back to Chapter 2 · Teacher’s answers: Chapter 2 · Complete key: Answers to Exercises PDF · Printed answers: appendices PDF
Lesson 1 (pages 43–45)
1. A conditional statement.
4. You live in the Ozarks.
6. Yes.
14. If an animal is a koala bear, then it eats only eucalyptus leaves.
16. If I don’t understand, then I ask questions.
21. If at first you don’t succeed, then try again.
24. Regions 1 and 2.
28. The second.
35. Statements c and d.
Lesson 2 (pages 47–49)
3. If a creature has two legs, then it is a goose.
5. You are not more than six feet tall.
9. If you do not know how to reason deductively.
13. They have the same meaning.
21. Yes. The converse must be true because this is a definition.
26. No.
28. It is the converse.
32. Sentence 2.
35. It is the converse.
Lesson 3 (pages 52–54)
2. If you keep quiet, others will think you are wise.
4. All Greeks are humans. All humans are mortals. Therefore, all Greeks are mortals.
7. No.
8. The hypothesis.
12. It also may be false.
16. A theorem.
18. If you go to Dallas, you will see the yellow rows of taxis.
22. 21.
26. Red. Because the label is wrong.
Lesson 4 (pages 57–59)
1. Contradiction.
3. Suppose that it would not speak foul language.
6. No.
10. It is the opposite of the theorem’s conclusion.
11. The earth is not flat.
14. That it is false.
p. 748
15. Beginning assumption: Suppose that the pupils can obey the teacher. Contradiction: There are 13 pupils at the black desks but only 12 brown desks. Conclusion: The pupils can’t obey the teacher.
Lesson 5 (pages 61–64)
3. You go around in circles.
6. Two points determine a line.
8. Theorems.
12. The points.
18. Converse.
20. True.
22. False.
26. A picul is 1,600 taels.
32. Statements 1 and 3.
37. Two points determine a line.
Lesson 6 (pages 67–70)
1. The length of the hypotenuse of a right triangle.
5. The area of a circle.
9. No.
12. , , , , and units.
13. square units.
18. 30°.
21. 70°.
24. No.
26. Approximately 50 mm².
32. Yes, because the sum of the other two angles could be 1°.
34. .
38. To the left.
Review (pages 71–74)
1. If something is a limerick, then it has five lines.
9. Collinear.
11. A postulate.
13. If it rains, then it pours.
18. 50°.
20. Three noncollinear points determine a plane.
23. Square.
32. Theorems.
34. 144 square units.
37. 20 ft.
41. Direct.
44. .
48. .
Algebra Review (page 76)
1. .
2. .
3. .
4. .
5. .
6. .
7. .
8. .
9. .
10. .
11. .
12. .
13. .
14. .
15. .
16. .
17. 10.
18. 8.
19. 3.
20. 6.
21. 13.
22. 9.
23. −7.
24. −5.
25. 60.
26. 0.
27. −12.
28. 37.
29. −2.
30. 4.5.
31. 12.
32. Any number.